A standardized​ exam's scores are normally distributed. In a recent​ year, the mean test score was 1521 and the standard deviation was 314. The test scores of four students selected at random are 1920​, 1290​, 2220​, and 1420. Find the​ z-scores that correspond to each value and determine whether any of the values are unusual

Answer:

D.

Step-by-step explanation:

Since a quadrilateral inscribed in a circle has its opposite angles adding up to 180°

So,

<MNO + <OLM = 180

82 + <OLM = 180

<OLM = 180-82

<OLM = 98°

Answer:

mean:12

Step-by-step explanation:

The population mean or sample mean as indicated in the given samples is 14

A mean in math is the average of a data set, found by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Mathematically,

Mean = Sum of the observations/number of observations

Now the given sample is,

17, 11, 8, 12, 22

So, Number of sample = 5

Thus, Mean = Sum of the sample /number of sample

Mean = (17 + 11 + 8 + 12 + 22) / 5

⇒ Mean = 70/5

⇒ Mean = 14

Thus, the population mean or sample mean as indicated in the given samples is 14

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Answer:

b = 87°

Step-by-step explanation:

In order to answer this question, we need to utilise an important angle fact which is angles in a quadrilateral add up to 360°

Using the information we can set up an equation to find the value of b

→ Form equation

63 + 140 + 70 + b = 360

→ Simplify

273 + b = 360

→ Minus 273 from both sides isolate b

b = 87°

Answer:

Hello!

The answer is 87 degrees!

I hope I was of help!  If not please let me know!  Thank you!

Step-by-step explanation:

Answer:

She can answer, after performing the hypothesis test, that there is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.

Step-by-step explanation:

She can statistically test the claim of the firefighters to see if it has statistical evidence.

This is a hypothesis test for the population mean.

The claim is that the city firefighters salary is significantly lower than the national average.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=38202\\\\H_a:\mu< 38202[/tex]

The significance level is 0.1.  Is less conservative than 0.05, for example, so if there is little evidence, the null hypothesis with be rejected.

The sample has a size n=27.

The sample mean is M=38073.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=575.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{575}{\sqrt{27}}=110.659[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38073-38202}{110.659}=\dfrac{-129}{110.659}=-1.17[/tex]

The degrees of freedom for this sample size are:

df=n-1=27-1=26

This test is a left-tailed test, with 26 degrees of freedom and t=-1.17, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.17)=0.127[/tex]

As the P-value (0.127) is bigger than the significance level (0.1), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the city firefighters salary is significantly lower than the national average.

Answer:

Step-by-step explanation:

If n represents the number of nickels, and the number of quarters is 4 times the number of nickels, then the number of quarters is represented by 4n.

The total value of the coins in cents is ...

  5(n) +25(4n) = 210

  105n = 210 . . . . . . . . collect terms

  n = 210/105 = 2 . . . . number of nickels

  4n = 4(2) = 8 . . . . . . number of quarters

Peggy has 2 nickels and 8 quarters.

Answer: The answer is (x-5)^2

Answer:

the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.

Step-by-step explanation:

Suppose, the weight of the alloy with 50% silver content is x  kilograms.

As, the weight of the mixed alloy should be 10 kilograms, so the weight of the alloy with 25% silver content will be:  kilograms

The percentage of silver content in the mixed alloy is 40%. So the equation will be calculated as

[tex]0.5x+0.25(10-x)=0.4\times10\\0.5x+2.5-0.25x=4\\0.25x=1.5\\\Rightarrow x=\frac{1.5}{0.25} = 6[/tex]

So, the amount of 50% silver alloy is 6 kilograms and the amount of 25% silver alloy is (10-6)= 4 kilograms.

Answer:

Step-by-step explanation:

Hello!

Given the variables

Y: standardized history test score in third grade.

X₁: final percentage in history class.

X₂: number of absences per student.

Determine the following multiple regression values.

I've estimated the multiple regression equation using statistics software:

^Y= a + b₁X₁ + b₂X₂

a= 118.68

b₁= 3.61

b₂= -3.61

^Y= 118.68 + 3.61X₁ - 3.61X₂

ANOVA Regression model:

Sum of Square:

SS regression: 25653.86

SS Total: 36819.23

F-ratio: 11.49

p-value: 0.0026

Se²= MMError= 1116.54

Hypothesis for the number of absences:

H₀: β₂=0

H₁: β₂≠0

Assuming α:0.05

p-value: 0.4645

The p-value is greater than the significance level, the decision is to not reject the null hypothesis. Then at 5% significance level, there is no evidence to reject the null hypothesis. You can conclude that there is no modification of the test score every time the number of absences increases one unit.

I hope this helps!

Answer:

[tex]P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)[/tex]

And we can find this probability using the complement rule and the normal standard table:

[tex]P(z>0.5)=1-P(z<0.5)= 1- 0.69146= 0.3085[/tex]

And the best solution would be:

c. 0.3085

Step-by-step explanation:

For this case we can convert all the values to inches in order to standardize the solution:

[tex] 5ft * \frac{12 in}{1ft}= 60 in[/tex]

[tex] 6ft * \frac{12 in}{1ft}= 72 in[/tex]

Let X the random variable that represent the heights of US mens, and for this case we know the distribution for X is given by:

[tex]X \sim N(70,4)[/tex]  

Where [tex]\mu=70[/tex] and [tex]\sigma=4[/tex]

We are interested on this probability

[tex]P(X>72)[/tex]

We can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(X>72)=P(\frac{X-\mu}{\sigma}>\frac{72-\mu}{\sigma})=P(Z>\frac{72-70}{4})=P(z>0.5)[/tex]

And we can find this probability using the complement rule and the normal standard table:

[tex]P(z>0.5)=1-P(z<0.5)= 1- 0.69146= 0.3085[/tex]

And the best solution would be:

c. 0.3085

Using the normal distribution, it is found that the probability that a randomly chosen American man is taller than 6 feet (72 inches) is equal to:

c. 0.3085

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

The probability of being taller than 72 inches is 1 subtracted by the p-value of Z when X = 72, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{72 - 70}{4}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085

Thus, option c.

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Answer:

LIFE: Your life purpose consists of the central motivating aims of your life—the reasons you get up in the morning. Purpose can guide life decisions, influence behavior, shape goals, offer a sense of direction, and create meaning. For some people, purpose is connected to vocation—meaningful, satisfying work. Also always be your self (:

Corona: I think corona depending on were you live will stop next year when they find a treatment for it.

Hope this helped!

Answer:

Your life is the most important thing. It shouldn't be worth 1 million dollars, or even 1 billion dollars, because it's worth everything.  

Corona can't really stop. It's a matter of the government to try to contain the virus, so it won't spread even further. I think the right time to reopen the economy is when we find a vaccine. But of course, places all over the U.S. are already reopening which will cause a spike in cases, therefore making our "self-isolation" even longer.

Answer:

A and F

Step-by-step explanation:

First we'll dilate it by a scale factor of 2. After that, we'll translate in 6 units left and 6 units up to map circle J onto circle K

Answer:

he will be 25

Step-by-step explanation:

36 monthly payments left/12 payments a year = 3 years. 22 + 3 = 25

Step-by-step explanation:

The graph of y = tan x is shown. We need to find what y equals when x = 0 (because in y = tan 0, x is replaced with 0)

So you can either find where x = 0 on the graph, or you can take the tangent of 0 to find your answer.

The value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is 0 and this can be determined by using the given graph.

Given :

The graph of [tex]y = \tan x[/tex].

The following steps can be used to determine the value of [tex]y = \tan 0[/tex] :

Step 1 - The graph of the trigonometric function [tex]y = \tan x[/tex] is given.

Step 2 - According to the given graph, at (x = 0) the value of y is also 0.

Step 3 - So, the value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is:

[tex]y = \tan 0[/tex]

[tex]y = 0[/tex]

The value of the trigonometric function [tex]y = \tan x[/tex] at (x = 0) is 0.

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Answer:

385 ways

Step-by-step explanation:

Given;

7 red balls

10 white balls

In how many ways can 4 balls be selected if there are more than 2 red balls.

Selecting 4 balls which must contain more than 2 red balls, will be 3 red balls and 1 white ball to make it 4 in total, or all the 4 balls selected will red balls.

= 3 red balls and 1 white ball  OR 4 red balls

= 7C₃ x 10C₁  + 7C₄

[tex]= \frac{7!}{4!3!} *\frac{10!}{9!1!} \ \ + \ \frac{7!}{3!4!} \\\\= (35*10) \ + \ 35\\\\= 350 \ + 35\\\\= 385 \ ways[/tex]

Therefore, there are 385 ways of selecting 4 balls, if there are more than 2 red balls.

Answer:

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%    

    Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

Step-by-step explanation:

We are given that a certain manufactured product is supposed to contain 23% potassium by weight.

A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.

Let [tex]\mu[/tex] = mean percentage of potassium by weight.

(a) Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 23%      {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 23%     {means that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

                                T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean percentage = 23.2

            s = sample standard deviation = 0.2

            n = sample of specimens = 10

So, the test statistics  =  [tex]\frac{23.2-23}{\frac{0.2}{\sqrt{10} } }[/tex]  ~ [tex]t_9[/tex]

                                     =  3.162

The value of t test statistic is 3.162.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.

(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) The P-value of the test statistics is given by;

            P-value = P( [tex]t_9[/tex] > 3.162) = 0.006 or 0.6%

(a) Null Hypothesis,  [tex]H_o:\mu[/tex]: = 23%    

   Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

The hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling or experimental error.

We are given that a certain manufactured product is supposed to contain 23% potassium by weight.

A sample of 10 specimens of this product had an average percentage of 23.2 with a standard deviation of 0.2.

Let  = mean percentage of potassium by weight.

(a) Null Hypothesis, [tex]H_o:\mu[/tex]:  = 23%      {means that the mean percentage is equal to 23 and the manufacturing process will not be re-calibrated}

Alternate Hypothesis,  [tex]H_A:\mu\neq[/tex]:   23%     {means that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

[tex]TS=\dfrac{X-\mu}{\frac{s}{\sqrt{n}}}[/tex]   ~ [tex]t_{n-1}[/tex]

where,  = sample mean percentage = 23.2

           s = sample standard deviation = 0.2

           n = sample of specimens = 10

So, the test statistics  =   [tex]\dfrac{23.2-23}{\frac{0.2}{\sqrt{10}}}[/tex] ~ [tex]t_g[/tex]

                                    =  3.162

The value of t test statistic is 3.162.

Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -2.262 and 2.262 at 9 degree of freedom for two-tailed test.

(b) Since our test statistic doesn't lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) The P-value of the test statistics is given by;

           P-value = P( [tex]t_g[/tex] > 3.162) = 0.006 or 0.6%

Hence ,

(a) Null Hypothesis,  [tex]H_o:\mu[/tex]: = 23%    

   Alternate Hypothesis, [tex]H_A:\mu\neq[/tex] : 23%

(b) We conclude that the mean percentage is  different from 23 and the manufacturing process will be re-calibrated.

(c) P-value is 0.6%.

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Answer:

$200

$100

Step-by-step explanation:

Darnell spends $100 dollars a week, if he reduces this spending by $50 a week, he will be able to save

$50 x 4 weeks in a months = $200

This, in a month he will be able to save $200.

Increasing his credit card payment by $200 to a total of $300...

since he now spends $50 per week now,

in a month he will spend $50 x 4 weeks = $200 and be able to save $100.

Answer:

This is the answer

Step-by-step explanation:

Answer:

A) 9

Step-by-step explanation:

R=7x+17

S=4x-6

Q=180-110=70

Answer:

x - 5 - (3/x+8)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the right answer, we just need to replace the given root in each expression and see which one gives zero.

[tex]f(x)=4x^{4} -7x^{2} +x+25\\f(-\frac{2}{5})= 4(-\frac{2}{5})^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+25=\frac{64}{625}-\frac{28}{25} -\frac{2}{5} +25 \approx 23.58[/tex]

[tex]f(x)=9x^{4}-7x^{2} +x+10=9(-\frac{2}{5} )^{4} -7(-\frac{2}{5} )^{2} +\frac{2}{5} +10 \approx 9.5[/tex]

[tex]f(x)=10x^{4}-7x^{2} +x+9=10(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+9 \approx 7.7[/tex]

[tex]f(x)=25x^{4}-7x^{2} +x+4=25(-\frac{2}{5} )^{4} -7(-\frac{2}{5})^{2} +(-\frac{2}{5})+4 \approx 3.12[/tex]

Therefore, neither expression satisfies the given rational root.

Answer:

D. f(x) = 25x^4 - 7x^2 + x + 4.

Step-by-step explanation:

The correct answer to your question is D.

Answer:

let the two number is x and y

x + y = 4 1/2 .....(i)

x - y = 3 1/4 ......(ii)

adding question (i) and (ii)

x + y = 9/2

x - y = 31/4

=> 2x = 31/4

x = 8/31

substituting the value x in equation 1

8/31 + y = 9/ 2

y = 9/2 - 8/31

y =203/62

the value of x = 8/31

y = 203/62

Answer:

[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]

Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194

Step-by-step explanation:

Let X the random variable of interest "number of adults with smartphones", on this case we now that:

[tex]X \sim Binom(n=7, p=0.53)[/tex]

The probability mass function for the Binomial distribution is given as:

[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]

Where (nCx) means combinatory and it's given by this formula:

[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]

And we want to find this probability:

[tex] P(X=5)[/tex]

Using the probability mass function we got:

[tex]P(X=5)=(7C5)(0.53)^5 (1-0.53)^{7-5}=0.194[/tex]

Then the probability that exactly 5 of them use their smartphones in meetings or classes is 0.194

Answer:

4037.3264$

Step-by-step explanation:

Total amount of money after 6 years:

A = P x (1 + rate)^time    

   = 9400 x ( 1 + (6/100)/4)^(6 x 4)    

   = 13437.3264$

=> Total amount of interest after 6 years:

I  = A - P = 13437.3264 - 9400 = 4037.3264$

Answer:

$9215.24

Step-by-step explanation:

Total Number of Computers=15

Number of New=11

Number of Refurbished Computers=4

[tex]P(NN)=\frac{11}{15} \times \frac{10}{14} = \frac{11}{21}\\P(NR)=\frac{11}{15} \times \frac{4}{14} = \frac{22}{105}\\P(RN)=\frac{4}{15} \times \frac{11}{14} = \frac{22}{105}\\P(RR)=\frac{4}{15} \times \frac{3}{14} = \frac{2}{35}[/tex]

The probability of one new and one refurbished =P(NR)+P(RN)

[tex]=\frac{22}{105}+ \frac{22}{105}\\=\frac{44}{105}[/tex]

Let X be the amount of profit earned on the purchase. The probability distribution of X is given as:

[tex]\left|\begin{array}{c|c|c|c|c}$Profit(X)& NN=\$10000 &NR=\$9600& RR=-\$800\\$P(X)&\dfrac{11}{21}&\dfrac{44}{105}&\dfrac{2}{35}\end{array}\right|[/tex]

(b) Expected Profit

[tex]\text{Expected Profit}=\sum X_iP(X_i)\\=(10000 \times \dfrac{11}{21}) +(9600 \times \dfrac{44}{105}) + (-800 \times \dfrac{2}{35})\\=\$9215.24[/tex]

The average profit of the store on the order is $9215.24.

Answer:

Step-by-step explanation:

The answer is 3x 987 colunm 2

Answer:

The value of X would be 4.

Answer:

x=4

Step-by-step explanation:

f(2)=3*2-1=5

g(x)=2x-3=5

2x=8

x=4

Answer:

[tex]<38,52>[/tex]

Step-by-step explanation:

[tex]u=<4,-3>\\v=<-2,5>\\w=<0,-6>[/tex]

We are required to express 7u-5v+w in the form <a,b>.

[tex]7u-5v+w =7<4,-3>-5<-2,5>+<0,-6>\\=<28,-21>-<-10,25>+<0,-6>\\=<28-(-10)+0, -21-25-6>\\=<38,52>\\$Therefore:$\\7u-5v+w=<38,52>[/tex]

Answer:

[tex]\dfrac{1}{27}[/tex]

Step-by-step explanation:

[tex]n^{-\frac{2}{3}}=9[/tex]

Rewrite:

[tex]\dfrac{1}{\sqrt[3]{n^2}}=9\\\\9\sqrt[3]{n^2}=1[/tex]

Cube both sides:

[tex]729n^2=1[/tex]

Divide both sides by 729:

[tex]n^2=\dfrac{1}{729}[/tex]

Take the square root of both sides:

[tex]n=\sqrt{\dfrac{1}{729}}=\dfrac{1}{27}[/tex]

Hope this helps!

Answer:

ROA = 7.77 percent

Step-by-step explanation:

Borland, Inc., has a profit margin of 5.6 percent on sales of $13.6 million

Thus, profit = 5.6% of  $13.6 million

profit = 5.6 / 100 *  $13.6 million = $0.7616 million

Profit is same as net income

Formula for ROA (return on asset) = net income/ total asset

total asset as given = $9.8 million

Thus, ROA = $0.7616/ $9.8 = 0.0777

ROA in percentage = 0.0777*100 = 7.77

Thus, ROA is 7.77 percent .